Depth-sensing indentation systems have been used for measuring modulus of various materials. Most commercially available depth-sensing indentation systems are also known as “nanoindentators”. When a nanoindentator is used, the indent size can be made to fall in the sub-micron range. As a result, ultra-small volumes of materials, e.g., second-phase particles in a matrix, thin-films deposited on substrates, etc., can be tested.
Unlike other conventional hardness testers, depth-sensing indentation systems use a depth-sensing machine to record the indenter displacement (or the “depth”) data as the indentation proceeds. Many well-known brand names of commercial nanoindenters, such as those manufactured by MTS Systems Corporation, Hysitron Inc. and CSEM Instruments, all use the Oliver-Pharr scheme in their analysis packages. In the Oliver-Pharr scheme, the load and the depth data can be analyzed to give the contact area as well as the contact stiffness between the indenter and the sample. The contact area can be used to compute the hardness of the sample, while the contact stiffness can be used to compute the elastic modulus of the sample.
In the Oliver-Pharr scheme, the contact stiffness between the indenter tip and the sample is estimated in an unloading process from the peak load assuming that the material recovery during the unloading process is purely elastic. The reduced modulus Er for the contact between the indenter tip and the sample is calculated from the contact stiffness S at the onset of the unloading process as follows:                               E          r                =                                            π                        2                    ⁢                      S                                          A                c                                                                        (        1        )            wherein Ac can be the contact area at full load. The contact area Ac is calculated from the contact depth hc by assuming a shape function of the indenter, i.e.,
Ac=f(hc),                               h          c                =                              h            max                    -                      ɛ            ⁢                                          P                max                            S                                                          (        2        )            wherein ε is a constant depending on the indenter geometry (e.g., ε=0.75 for the Berkovich tip). The reduced modulus Er is related to the sample Young's modulus as follows:                               1                      E            r                          =                                            1              -                              v                s                2                                                    E              s                                +                                    1              -                              v                t                2                                                    E              t                                                          (        3        )            wherein Es=Young's modulus of the sample object, vs=Poisson's ratio of the sample object, Et=Young's modulus of the indenter tip, vt=Poisson's ratio of the indenter tip. In the Oliver-Pharr scheme, the contact stiffness to be used in the above equations (1) and (2) is the observed (or apparent) contact stiffness S, at the onset of the unloading process.
In reality, however, significant creep can occur at the peak load even for metals at room temperature after long holding periods. As shown in FIGS. 2(a) and 2(b), the indenter displacement continues to creep in both cases even after a long holding period of ten (10) minutes. The displacement rate appears to settle to a steady value of about 0.020 nm/s in Al and about 0.009 nm/s in Ni3Al. Such a significant creep effect at the peak load can strongly affect the subsequent unloading behavior, especially when the unloading rate is not high enough.
In the extreme case where a creep dominates an elastic recovery at the onset of the unloading process, the load-displacement curve can even exhibit a “nose”, such as shown in FIG. 4a for an aluminum sample object. Load schedules (i) to (iii), such as those shown in FIG. 3b, represent three similar indentation experiments on the same aluminum sample. Load schedule (i) has a very rapid unloading rate. Load schedules (ii) and (iii) have the same unloading rate, which is slower than the unloading rate in load schedule (i). On the other hand, load schedules (i) and (ii) have a short load holding period before the unloading process, while load schedule (iii) has a longer load holding period. A conspicuous “nose”, such as that shown in FIG. 4a, appears in the unloading curve for load schedule (ii). The “nose” disappears when the unloading rate is increased, such as shown in the unloading curve for load schedule (i), or when the load holding period before unloading is lengthened, such as shown in the unloading curve for load schedule (iii).
When a “nose” occurs, the elastic modulus cannot be accurately calculated using the Oliver-Pharr scheme, because the apparent contact stiffness Su becomes negative. Moreover, even if a “nose” does not occur, the presence of creep can cause serious errors in the estimation of the elastic modulus, if the creep effect is not corrected. Moreover, creep effects can become significant in certain circumstances, such as where an indentation is performed at a temperature of a significant fraction (e.g., more than 40%) of the absolute melting temperature or where a nano-sized indentation is performed by exerting a very large pressure on the sample.
The present invention provides a method for measuring elastic properties, such as the elastic modulus of an object, that avoids the above problems. Moreover, the present invention provides a method for measuring the elastic modulus of a solid material by depth-sensing indentation where the creep effect is corrected. Furthermore, the present invention provides a method for correcting a creep effect occurred when measuring elastic properties of a solid material by depth-sensing indentation.